Chapter 7.6, Problem 35E

To determine

To calculate: The length and the width of the base of The Parthenon, in Athens, Greece.

Answer to Problem 35E

The $width$ is $31m$ and length of base is $70m$ .

Explanation of Solution

Given information: Length of the rectangular base is $8meters$ more than twice its width, area of the base is $2170sq.m$ .

Calculation:

Given area of base $=2170sq.m-(i)$

Area of rectangle $=length\times width-(ii)$

As per given information, $length=2(width)+8-(iii)$

Combining equations $(i)$ and $(ii)$

  $length\times width=2170-(iv)$

Putting $(iii)$ in $(iv)$ and $\text{'}width\text{'}=w$

  $(2(w)+8)\times w=2170$

  $\Rightarrow 2w^2+8w=2170$

Factoring out GCF

  $\begin{array}{l}2(w^2+4w-1085)=0\\ \Rightarrow w^2+4w-1085=0\end{array}$

Writing the equation with left side factored and solving for $\text{'}width\text{'}=w$ ,

  $w(w+35)-31(w+35)=0$

  $\Rightarrow (w+35)(w-31)=0$

  $\Rightarrow w=31$ (Width can’t be negative)

Putting above stated value of width in equation $(iii)$ ,

  $length=2(31)+8$

  $=62+8$

  $=70meters$

Thus, the $width$ is $31m$ and length is $70m$ .